(8n-6p)(7n-10p)=

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Solution for (8n-6p)(7n-10p)= equation: 


Simplifying
(8n + -6p)(7n + -10p) = 0

Multiply (8n + -6p) * (7n + -10p)
(8n * (7n + -10p) + -6p * (7n + -10p)) = 0
((7n * 8n + -10p * 8n) + -6p * (7n + -10p)) = 0

Reorder the terms:
((-80np + 56n2) + -6p * (7n + -10p)) = 0
((-80np + 56n2) + -6p * (7n + -10p)) = 0
(-80np + 56n2 + (7n * -6p + -10p * -6p)) = 0
(-80np + 56n2 + (-42np + 60p2)) = 0

Reorder the terms:
(-80np + -42np + 56n2 + 60p2) = 0

Combine like terms: -80np + -42np = -122np
(-122np + 56n2 + 60p2) = 0

Solving
-122np + 56n2 + 60p2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-61np + 28n2 + 30p2) = 0

Factor a trinomial.
2((7n + -10p)(4n + -3p)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7n + -10p)' equal to zero and attempt to solve:

Simplifying
7n + -10p = 0

Solving
7n + -10p = 0

Move all terms containing n to the left, all other terms to the right.

Add '10p' to each side of the equation.
7n + -10p + 10p = 0 + 10p

Combine like terms: -10p + 10p = 0
7n + 0 = 0 + 10p
7n = 0 + 10p
Remove the zero:
7n = 10p

Divide each side by '7'.
n = 1.428571429p

Simplifying
n = 1.428571429p

Subproblem 2
Set the factor '(4n + -3p)' equal to zero and attempt to solve:

Simplifying
4n + -3p = 0

Solving
4n + -3p = 0

Move all terms containing n to the left, all other terms to the right.

Add '3p' to each side of the equation.
4n + -3p + 3p = 0 + 3p

Combine like terms: -3p + 3p = 0
4n + 0 = 0 + 3p
4n = 0 + 3p
Remove the zero:
4n = 3p

Divide each side by '4'.
n = 0.75p

Simplifying
n = 0.75p
Solution
n = {1.428571429p, 0.75p}

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